Question Number 211703 by MrGaster last updated on 17/Sep/24
$$ \\ $$$$\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{quadruple}\: \\ $$$$\mathrm{integralas}\:\mathrm{follows}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{I}}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\boldsymbol{{x}}} \int_{\mathrm{0}} ^{\boldsymbol{\mathrm{y}}} \int_{\mathrm{0}} ^{\boldsymbol{{z}}} \frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} +\boldsymbol{{w}}^{\mathrm{2}} \right)}{\mathrm{1}+\boldsymbol{{w}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}} }\boldsymbol{{dw}}\:\boldsymbol{{dz}}\:\boldsymbol{\mathrm{dy}}\:\boldsymbol{{dx}} \\ $$$$ \\ $$
Commented by MrGaster last updated on 17/Sep/24
Calculate the integrals in the areas 0≤w≤z, 0≤z≤y, 0≤y≤x, 0≤x≤1, where the function of the integral is sin (x 2+y 2+z 2+w 2) divided by (1+w^2+z^2).
Commented by BHOOPENDRA last updated on 18/Sep/24
$${I}\approx\mathrm{0}.\mathrm{41176}?? \\ $$